From climate change to health inequity, humankind faces complex societal challenges that aviation can both exacerbate and help to alleviate. In this paper we describe our approach to identifying and approaching complex societal challenges with existing or potential ties to aviation as part of the NASA Convergent Aeronautics Solutions (CAS) project. We detail three example challenges that we have done preliminary work on: enabling access to healthcare, supporting resilient rural communities, and ensuring supply chain wellness. Our approach to understanding and addressing such challenges involves iterative human-centered, systems-oriented, and futures-based design. We provide a discussion of cross-cutting characteristics of complex societal challenges that appear fruitful for aviation to address and detail the lessons we have learned thus far in approaching such challenges.